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Session S06 - Interacting Stochastic Systems

Tuesday, July 13, 14:00 ~ 14:35 UTC-3

Random walk in a field of weakly killing exclusion particles

Dirk Erhard

Universidade Federal da Bahia, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Consider a simple random walk, and independently of it the simple symmetric exclusion process on $\mathbb{Z}^d$. The random walk gets killed at rate epsilon when it shares a site with an exclusion particle. Using the relation to the parabolic Anderson model and the theory of regularity structures, I will present exact asymptotics for the survival probability of the random walk as epsilon tends to zero in dimension $d=3$. To establish these, precise bounds on the joint cumulants of the exclusion process are needed, which hold as soon as $d\geq 3$. I will also discuss what is missing to establish the corresponding result in $d=2$.

Joint work with Martin Hairer (Imperial College London).

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